Page 66 - Solutions Manual to accompany Electric Machinery Fundamentals

I AP = 20.96?-60.5° A I AS = 363?-60.5°
A A
I CS = 363?59.5° A
B A C .
I BP = 20.96?-180.5° + I ?B = 363?-120.5° A
A + + -
V A = 8314?0° V V AS = 480?0° V V BS = 480?-120° V
- - - +
I n = 20.96?59.5° A V B = 8314 ?-120° V I BS = 363?-180.5° A
n B .

The real and reactive powers supplied by each transformer are calculated below:
P  V I cos   480 V 363 A cos 0     60.5     85.8 kW
A AS A  
Q  V I  cos   480 V 363 A sin 0      60.5     151.7 kvar
A AS A  
P  V I cos   480 V 363 A cos   120    120.5     174.2 kW
B BS  B  
Q  V I sin   480 V 363 A sin    120    120.5     1.5 kvar
B BS  B  
Notice that the real and reactive powers supplied by the two transformers are radically different, put the
apparent power supplied by each transformer is the same. Also, notice that the total power P  P
B
A
supplied by the transformers is equal to the power consumed by the loads (within roundoff error), while
the total reactive power Q  Q B supplied by the transformers is equal to the reactive power consumed by
A
the loads.
2-20. A 50-kVA 20,000/480-V 60-Hz single-phase distribution transformer is tested with the following results:
Open-circuit test Short-circuit test
(measured from secondary side) (measured from primary side)
V OC = 480 V V SC = 1130 V
I OC = 4.1 A I SC = 1.30 A
P OC = 620 W P SC = 550 W

(a) Find the per-unit equivalent circuit for this transformer at 60 Hz.
(b) What is the efficiency of the transformer at rated conditions and unity power factor? What is the
voltage regulation at those conditions?
(c) What would the ratings of this transformer be if it were operated on a 50-Hz power system?
(d) Sketch the equivalent circuit of this transformer referred to the primary side if it is operating at 50
Hz.
(e) What is the efficiency of the transformer at rated conditions on a 50 Hz power system, with unity
power factor? What is the voltage regulation at those conditions?
(f) How does the efficiency of a transformer at rated conditions and 60 Hz compare to the same
physical device running a 50 Hz?

SOLUTION
(a) The base impedance of this transformer referred to the primary side is

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